Problem: Hungry Harry is a giant ogre with an appetite that fluctuates throughout the day. $H(t)$ models the weight of sheep (in $\text{kg}$ ) that Harry would like to swallow $t$ hours after he wakes up. Here, $t$ is entered in radians. $H(t) = 12\sin\left(\dfrac{2\pi}{24}t\right) + 15$ What is the second time after Harry wakes up that he feels like consuming $17{\text{ kg}}$ of sheep? Round your final answer to the nearest tenth of an hour.
Answer: Converting the problem into mathematical terms $H(t) = 12\sin\left({\dfrac{2\pi}{24}}t\right) + 15$ has a period of $\dfrac{2\pi}{{\scriptsize\dfrac{2\pi}{24}}}=24$ hours. We want to find the second solution to the equation $H(t)=17$ within the period $0<t<24$. The answer The equation's two solutions within the desired period (rounded to the nearest tenth of an hour) are $0.6$ and $11.4$. Therefore, the second time that Harry feels like consuming $17{\text{ kg}}$ of sheep after he wakes up is after $11.4$ hours.